If f x + 2 f 1 x = 3 x , x ≠ 0 , and S = x ∈ R : f x = f - x , then S

Contains more than two elements

The domain of the definition of the function f x = 1 4 - x 2 + l o g 10 x 3 - x is:

- 2 , - 1 ∪ - 1 , 0 ∪ 2 , ∞

EASY

Earn 100

Let $f (x)$ be a non-zero function satisfying $f (x + y) = f (x) f (y),$ $\forall x, y \in R$ .Then $f (0)$ is equal to

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Important Questions on Relations and Functions

MEDIUM

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let

f : [0,1] \to R

be such that

f (x y) = f (x) \cdot f (y),

for all

x, y \in [0,1],

and

f (0) \neq 0 .

y = y (x)

satisfies the differential equation,

\frac{d y}{d x} = f (x)

with

y (0) = 1

then

y (\frac{1}{4}) + y (\frac{3}{4})

is equal to:

HARD

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

The value of

n \in I

for which the function

f (x) = \frac{\sin n x}{\sin (\frac{x}{n})}

has

4 π

as its period is:

MEDIUM

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let,

f : R \to R

be a function such that

f (x) = x^{3} + x^{2} f^{'} (1) + x f^{"} (2) + f^{'''} (3), \forall x \in R .

Then

f (2)

equals

HARD

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let

a, b, c \in R

. If

f (x) = a x^{2} + b x + c

is such that

a + b + c = 3

and

f (x + y) = f (x) + f (y) + x y, \forall x, y \in R

, then

\sum_{n = 1}^{10} f (n)

is equal to:

EASY

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

f (x) = \frac{1 + x}{1 - x}; x \neq 1

, then

f (x) \cdot f (y) =

_____

HARD

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

The range of the polynomial

P (x) = 4 x^{3} - 3 x

x

varies over the interval

(- \frac{1}{2}, \frac{1}{2})

EASY

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

f : R - \{2\} \to R

is a function defined by

f (x) = \frac{x^{2} - 4}{x - 2},

then range is

MEDIUM

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

f (x) + 2 f (\frac{1}{x}) = 3 x, x \neq 0,

and

S = \{x \in R : f (x) = f (- x)\}

, then

S

EASY

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

The range of the function

f (x) = \frac{1}{2 - \cos 3 x}

EASY

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

The domain of the definition of the function

f (x) = \frac{1}{4 - x^{2}} + {l o g}_{10} (x^{3} - x)

is:

MEDIUM

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let

f : x \to y

be such that

f (1) = 2

and

f (x + y) = f (x) f (y)

for all natural numbers

x

and

y

.

\sum_{k = 1}^{n} f (a + k) = 16 (2^{n} - 1)

then

a

is equal to

EASY

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

f : z \to z

is defined by

f (x) = x^{9} - 11 x^{8} - 2 x^{7} + 22 x^{6} + x^{4} - 12 x^{3} + 11 x^{2} + x - 3 \forall x \in z

, then

f (11) =

EASY

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let

f : (- 1, 1) \to (- 1, 1)

be continuous,

f (x) = f (x^{2})

for all

x \in (- 1, 1)

and

f (0) = \frac{1}{2}

,

then the value of

4 f (\frac{1}{4})

HARD

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let

f

be a continuous function defined on

[0, 1]

such that

\int_{0}^{1} f^{2} (x) d x = {(\int_{0}^{1} f (x) d x)}^{2}

. Then the range of

f

EASY

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let

f : R \to R

satisfy

f (x) f (y) = f (x y)

for all real numbers

x

and

y

.

f (2) = 4

,

then

f (\frac{1}{2}) =

HARD

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let

f : (1, 3) \to R

be a function defined by

f (x) = \frac{x [x]}{1 + x^{2}},

where

[x]

denotes the greatest integer

\leq x .

Then the range of

f

HARD

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let

\sum_{k = 1}^{10} f (a + k) = 16 (2^{10} - 1),

where the function

f

satisfies

f (x + y) = f (x) f (y)

for all natural numbers

x, y

and

f (1) = 2 .

Then the natural number

a

is:

EASY

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

Let

f : [2, \infty) \to R

be the function defined by

f (x) = x^{2} - 4 x + 5

, then the range

EASY

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

f (x) = 2 \sin x, g (x) = \cos^{2} x

, then

(f + g) \frac{π}{3} =

MEDIUM

Mathematics>Algebra>Relations and Functions>Algebra of Real Functions

f (x) = \frac{x}{x - 1}, f (3 x)

in terms of

f (x)

Let fx be a non-zero function satisfying fx+y=fx fy, ∀ x, y∈R .Then f0 is equal to

Important Questions on Relations and Functions

Learn and Prepare for any exam you want !

Let $f (x)$ be a non-zero function satisfying $f (x + y) = f (x) f (y),$ $\forall x, y \in R$ .Then $f (0)$ is equal to